Problem: Rewrite as a simplified fraction. ${0.7\overline{83} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 783.8383...\\ 10x &= 7.8383...\end{align*}}$ Subtracting the two equations, we have: ${990x = 776}$ ${x = \dfrac{776}{990}} $ ${x = \dfrac{388}{495}} $